Finite Group Databasebeta

← #14664627

Subgroups — #14664627

Order 2816.

280 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079361C211yesmaximal, characteristic
2#13068765C211yesmaximal, characteristic
3#13066611C212yesmaximal
4#13066605C212yesmaximal
5C11×#2165C211yesmaximal, characteristic
6#10623001—21no—
7C4×C11×M16C2211yescharacteristic
8#10622750—21no—
9#10622750C2212yes—
10#10622329—21no—
11#10622329C412yescomplemented
12#10622312C411yescharacteristic, complemented
13#10622294—21no—
14#10622293C411yescharacteristic, complemented
15C11×#364—21no—
16C11×#349C2212yes—
17C11×#347—21no—
18C11⋊#338C2211yescharacteristic
19#10622195C2211yescharacteristic
20#10622194—21no—
21#10622161—21no—
22C2×C11×M16D411yescharacteristic
23C2×C11×M16C2311yescharacteristic
24C2×C42×C11D411yescharacteristic
25#66979—21no—
26#66979—41no—
27#66977—22no—
28#66977—41no—
29C2×#4318—21no—
30C2×Dic44—21no—
31C2×Dic44C2×C412yes—
32#66923—41no—
33#66922—21no—
34#66922—21no—
35C4×Dic22—22no—
36C4×Dic22—41no—
37C11×M32—22no—
38C11×#97C2×C411yescharacteristic
39C11×#97D411yescharacteristic
40C4×C8×C11C2×C411yescharacteristic
41C4×C8×C11D411yescharacteristic
42#66881—21no—
43#66881C2×C412yes—
44#66880—22no—
45#66880—22no—
46#11838—111nomaximal, Sylow
47C22×C4×C11—21no—
48C22×C4×C11C2×D411yescharacteristic
49C2×Dic22—22no—
50C2×Dic22—41no—
51C11×M16—41no—
52C11×M16—41no—
53C2×C8×C11C22⋊C411yescharacteristic
54C2×C8×C11C22⋊C411yescharacteristic
55C2×C8×C11C22×C411yescharacteristic
56C2×C8×C11C2×D411yescharacteristic
57C42×C11—21no—
58C42×C11C22⋊C411yescharacteristic
59C42×C11C22⋊C411yescharacteristic
60C22⋊Dic11—42no—
61C22⋊Dic11—41no—
62C4⋊Dic11—22no—
63C4⋊Dic11—41no—
64C4⋊Dic11—41no—
65C4⋊Dic11—41no—
66C4⋊Dic11—41no—
67Dic11⋊C4—42no—
68Dic11⋊C4—42no—
69C4×Dic11—42no—
70C4×Dic11—41no—
71#4318—41no—
72#4318—41no—
73C2×C11⋊C8—41no—
74Dic44—42no—
75Dic44—42no—
76C11×C16—42no—
77#3185—111no—
78#2165D1111yescharacteristic
79#1841—111no—
80#1342—112no—
81#1340—112no—
82C23×C11AGL(1,ℤ/8)11yescharacteristic
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—42no—
88C2×C4×C11C2×C22⋊C411yescharacteristic
89C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
90C2×Dic11—42no—
91C2×Dic11—42no—
92C2×Dic11—81no—
93Dic22—42no—
94Dic22—42no—
95Dic22—82no—
96C8×C11—21no—
97C8×C11—21no—
98C8×C11—21no—
99C8×C11—21no—
100C11⋊C8—81no—
101#533—221no—
102#498—111no—
103#494—111no—
104#487—221no—
105#470—112no—
106#470—221no—
107#441—112no—
108#441—221no—
109C4×M16C2×D1111yescharacteristic
110#364—21no—
111#349C2×D1112yes—
112#347—21no—
113#344—221no—
114#339—221no—
115#338—111no—
116H(3,ℤ/4)—111no—
117C22×C11—21no—
118C22×C11—41no—
119C22×C11#41811yescharacteristic
120C4×C11—22no—
121C4×C11—21no—
122C4×C11—41no—
123C4×C11#41011yescharacteristic
124C4×C11#42111yescharacteristic
125Dic11—82no—
126Dic11—82no—
127Dic11—161no—
128C2×Q16—112no—
129C2×Q16—221no—
130C2×M16—221no—
131C2×M16D4411yescharacteristic
132C2×M16C22×D1111yescharacteristic
133C4⋊Q8—221no—
134C4⋊Q8—221no—
135#125—441no—
136C22⋊Q8—222no—
137C22⋊Q8—441no—
138C4×Q8—222no—
139C4×Q8—441no—
140#117—221no—
141#117—441no—
142C2×C42D4411yescharacteristic
143M32—22no—
144#106—112no—
145#106—221no—
146#103—222no—
147#103—222no—
148#97C4×D1111yescharacteristic
149#97C22⋊D1111yescharacteristic
150C4×C8C4×D1111yescharacteristic
151C4×C8C22⋊D1111yescharacteristic
152C2×C11—21no—
153C2×C11—41no—
154C2×C11#151411yescharacteristic
155C2×Q8—222no—
156C2×Q8—441no—
157C22×C4—21no—
158C22×C4C2×D4411yescharacteristic
159Q16—442no—
160Q16—442no—
161M16—41no—
162M16—41no—
163M16—441no—
164M16—441no—
165C2×C8—441no—
166C2×C8(C2×D11)⋊C411yescharacteristic
167C2×C8(C2×D11)⋊C411yescharacteristic
168C2×C8C2×C4×D1111yescharacteristic
169C2×C8C2×C22⋊D1111yescharacteristic
170C4⋊C4—222no—
171C4⋊C4—441no—
172C4⋊C4—441no—
173C4⋊C4—442no—
174C4⋊C4—441no—
175C4⋊C4—441no—
176C4⋊C4—442no—
177C22⋊C4—442no—
178C22⋊C4—441no—
179C42—21no—
180C42—442no—
181C42—441no—
182C42(C2×D11)⋊C411yescharacteristic
183C42(C2×D11)⋊C411yescharacteristic
184C16—42no—
185C11#1183811yescharacteristic, complemented, Sylow
186C23#6696111yescharacteristic
187Q8—442no—
188Q8—442no—
189Q8—882no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—442no—
196C2×C4—442no—
197C2×C4—881no—
198C2×C4#6696111yescharacteristic
199C2×C4C2×(C2×D11)⋊C411yescharacteristic
200C8—21no—
201C8—21no—
202C8—21no—
203C8—21no—
204C8—881no—
205C22—21no—
206C22—41no—
207C22#1062274411yescharacteristic
208C4—22no—
209C4—21no—
210C4—41no—
211C4—882no—
212C4—882no—
213C4—1761no—
214C4#1062261911yescharacteristic
215C4#1062275211yescharacteristic
216C2—21no—
217C2—41no—
218C2#1306716411yescharacteristic
subgroupG/H
centerC2#13067164
commutatorC2×C8×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#2165C2
socleC2×C11#1514
prime radicalC23×C11AGL(1,ℤ/8)
cosocleC2×C11×M16C23
hypercenter#2165D11
hypocenterC11#11838
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
11. #10622329C4semidirect
12. #10622312C4semidirect
14. #10622293C4semidirect
185. C11#11838semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130793612
#130687652
#130666112
#130666052
C11×#21652
#1183811